Imaging apparatus that utilize relatively high energy radiation such as x-ray and gamma rays are widely used to obtain images of subject matter more or less opaque to electromagnetic energy in the visual spectrum. For example, x-ray imaging technology has been employed in a wide range of applications from medical imaging to detection of unauthorized objects or materials in baggage, cargo or other containers. X-ray imaging typically includes passing radiation (i.e., x-rays) through an object to be imaged, X-rays from a source passing through the object are attenuated according to the various absorption characteristics of the material which the radiation encounters. By measuring the extent of attenuation of radiation that exits the object (e.g., by comparing the intensity of radiation entering and exiting the object), information related to the density distribution of the object may be obtained.
Computer tomography (CT) techniques typically involve capturing x-ray attenuation information from a plurality of angles about an object being imaged to reconstruct a three dimensional (3D) volume image of the object. For example, to obtain attenuation information about an object, a radiation source and a detector (or an array of detectors) responsive to the radiation may be arranged about the object. Each detector in the array, for example, may generate an electrical signal proportional to the intensity of radiation impinging on a surface of the detector. The source and detector may be rotated around the object to expose the object to radiation at a desired number of angular orientations.
At each orientation, referred to as a view angle, the detector signal generated by each detector in the array indicates the total absorption (i.e., attenuation) incurred by material substantially in a line between the radiation source and the detector. Therefore, the array of detection signals at each view angle records the projection of the object onto the detector array at the associated view angle. For example, using a 2D detector array, the resulting detector signals represent the 2D density projection of the object on the detector array at the corresponding view angle. The signals generated by the detectors form, at least in part, projection data (or view data) of the object.
Projection data obtained from multiple view angles about the object may be used to compute a density distribution of the object (i.e., to determine density values for locations within the object). The process of converting projection data (i.e., attenuation as a function of view angle) to density data (i.e., density as a function of location within the object) is referred to as reconstruction, That is, density values are reconstructed from information contained in the projection data. Typically, density values are expressed as image data, i.e., pixel or voxel values in two-dimensional (2D) and three-dimensional (3D) images, respectively.
Many techniques have been developed for reconstructing projection data into image data. For example, filtered back-projection is a widely used technique to form images from projection data obtained from single or multiple view angles. In general, reconstruction methods are based upon an assumed relationship between the intensity of radiation impinging on a detector and the integral of the density distribution of the object along the line from the radiation source to the detector. For example, the intensity-density relationship of radiation penetrating matter may be characterized as:I=I0e−μ(z)  (1),where I0 is the intensity of the radiation emitted from the radiation source before penetrating the material, I is the intensity of radiation having penetrated the material through a thickness z, and μ is a material specific linear absorption coefficient related to the density of the material. The term “intensity,” with respect to radiation, refers to the amount of radiation present in or passing through a given volume per unit of time, and is thus a measure of radiation flux. The difference between I and I0 is assumed to be the result of absorption by material substantially along a ray between the radiation source providing the radiation at intensity I and the detector detecting the radiation at intensity I0. Thus, the relationship in Equation 1 can be used to compute the integral of the μ values over z along the ray between source and detector. This measurement approximates the total density of material situated along the ray between the source and detector.
In radiographic images (i.e., images reconstructed from projection data obtained at a single view angle), the total density approximation may be used as, or may be proportional to, the corresponding pixel value in the reconstructed image. Thus, the appropriate computation may be made along each ray from the radiation source to each detector location to form an image of the object at the single view angle. In CT images, projection data from multiple view angles are obtained. As a result, the various rays along which integral μ values are obtained will intersect at different locations within the object, thus providing additional information about discrete μ values at the intersection points. Accordingly, the projection data from multiple view angles may be used to differentiate individual μi values along the ray to provide information in an additional dimension. That is, rather than having a single integral μ value along each ray, the information in intersecting rays from the multiple view angles may be correlated to determine μi values at discrete locations along each ray to provide a tomographic reconstruction of the density distribution.